Growing up we never used "Road" we just said "County (letter)" Probably because the signs themselves never say Road or Highway (at least usually, back in the day, I haven't paid attention recently).

I like the system. It helps reduce confusion in terms of what the "main" (state/interstate) vs the local.

I think part of it is that “the highway” now usually refers to a nice highway or freeway somewhere nearby, and if you say “the county X” without specifics which one, you’re likely to say “county road”.